Modeling and Mathematical Investigation of Blood-Based Flow of Compressible Rate Type Fluid with Compressibility Effects in a Microchannel

In this investigation, the compressibility effects are visualized on the flow of non-Newtonian fluid, which obeys the stress–strain relationship of an upper convected Maxwell model in a microchannel. The fundamental laws of momentum and mass conservation are used to formulate the problem. The governing nonlinear partial differential equations are reduced to a set of ordinary differential equations and solved with the help of the regular perturbation method assuming the amplitude ratio (wave amplitude/half width of channel) as a flow parameter. The axial component of velocity and flow rate is computed through numerical integration. Graphical results for the mean velocity perturbation function, net flow and axial velocity have been presented and discussed. It is concluded that the net flow rate and (Formula presented.) increase in case of the linear Maxwell model, while they decrease in case of the convected Maxwell model. The compressibility parameter shows the opposite results for linear and upper convected Maxwell fluid.